Proposition 3 (PAC Learning [1]}) 
Let \(\epsilon , \delta \in \mathbb {R}^+\) . If number of sampling points is \(N\ge \frac{1}{\epsilon }\ln \frac{1}{\delta }\) , where the sample points \(\Gamma \)  are drawn from a distribution \(\mathcal {P}\) , then, with probability greater than \(1 - \delta \) , a linear separator \((a,b)\)  has an error \(\texttt {err}_{\mathcal {P}}\)  of less than \(\epsilon \) , where the error of a pair \((a, b)\)  is defined as \(\texttt {err}_{\mathcal {P}}(a,b)=\mathcal {P}({(x,y)\in \Gamma |x>ay+b})\) .

